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On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil Cover

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

Studia Geotechnica et Mechanica
Volume 42 (2020): Issue 2 (June 2020)
By: Marcin Chwała  
Open Access
|Jun 2020

Figures & Tables

Figure 1

Failure geometry for a rough foundation base in the case of rectangular foundation. More details on failure geometry can be found in Chwała (2019a).
Failure geometry for a rough foundation base in the case of rectangular foundation. More details on failure geometry can be found in Chwała (2019a).

Figure 2

Value of bearing capacity during simulation within optimization procedure
Value of bearing capacity during simulation within optimization procedure

Figure 3

Flow chart of the numerical algorithm. Detailed descriptions of the steps are in the text.
Flow chart of the numerical algorithm. Detailed descriptions of the steps are in the text.

Figure 4

Comparison of bearing capacity variation coefficients obtained by the method proposed in this study (constant covariance matrix) with standard algorithm (individual covariance matrix, Chwała (2019a)). The relative differences between both approaches are below 5%, which is sufficient for the purpose of this study. A detailed description is in the text.
Comparison of bearing capacity variation coefficients obtained by the method proposed in this study (constant covariance matrix) with standard algorithm (individual covariance matrix, Chwała (2019a)). The relative differences between both approaches are below 5%, which is sufficient for the purpose of this study. A detailed description is in the text.

Figure 5

Mean value, standard deviation and variation coefficient of bearing capacity as a function of simulation number N. The square foundation is assumed with geometry parameters and fluctuation scales detailed in the figure.
Mean value, standard deviation and variation coefficient of bearing capacity as a function of simulation number N. The square foundation is assumed with geometry parameters and fluctuation scales detailed in the figure.

Figure 6

Graph for reading Dp value for ratios θv ⁄ b ∈ [2.0,1.0] and θv ⁄ b∈ [0.25,0.125]. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.
Graph for reading Dp value for ratios θv ⁄ b ∈ [2.0,1.0] and θv ⁄ b∈ [0.25,0.125]. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.

Figure 7

Graph for reading Dp value for ratios θv ⁄ b ∈ [1.0,0.25]. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.
Graph for reading Dp value for ratios θv ⁄ b ∈ [1.0,0.25]. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.

Figure 8

Graph for reading Dp value for an infinite horizontal fluctuation scale.
Graph for reading Dp value for an infinite horizontal fluctuation scale.

Figure 9

Illustration of example scenarios. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.
Illustration of example scenarios. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.

Figure 10

Illustration of example scenarios. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.
Illustration of example scenarios. Note that the colour in the legend indicates θv ⁄ b and the line type (coloured on black in the legend) indicates θv ⁄ b.

Exemplary usage of the graphs proposed in this study_ Detailed descriptions are in the text_

No.Scenario descriptionCOVp read from graphs [-]COVp determined by numerical analyses [-]Difference [%]
a [m]b [m]θv [m]θh [m]COVcu [-]
12.02.00.612.00.60.410.435−6.1%
210.01.51.05.00.40.2260.210+7.1%
320.00.90.83.01.00.290.311−7.2%
425.01.81.21.20.50.0570.052+8.7%
52.01.01.52.00.70.4510.458−1.5%
625.03.00.510.01.00.290.280+3.4%
73.03.00.40∞0.240.130.1300.0%
820.01.00.47∞0.510.400.403−0.7%

Coefficients from Eq_ (A_2)–Eq_ (A_5) for rough and smooth foundation base_ Note that the undrained shear strengths ci are defined individually for each dissipation region (for more details see Chwała, 2019a)_

Coeff.Expression
m1c1 cot β2 + 2c21(α2 + β2) + c2 cot α2
m2c6 cot α2 + 2c24(α2 + β2) + c5 cot β2
m3c8 cot α2 + 2c23(α2 + β2) + c7 cot β2
m4c3 cot β3 + 2c22(α3 + β3) + c4 cot α3
m5c10 cot α3 + 2c26(α3 + β3) + c9 cot β3
m6c12 cot α3 + 2c25(α3 + β3) + c11 cot β3
m7c16 cot α1 + 2c28(α1 + β1) + c14 cot β1
m8c15 cot α1 + 2c27(α1 + β1) + c13 cot β1
m9c20 cot α4 + 2c30(α4 + β4) + c19 cot β4
m10c18 cot α4 + 2c29(α4 + β4) + c17 cot β4
n11+b22d12(sinβ2)2\sqrt {1 + {{b_2^2 } \over {d_1^2 \left( {\sin \beta _2 } \right)^2 }}}
n21+b22d22(sinβ2)2\sqrt {1 + {{b_2^2 } \over {d_2^2 \left( {\sin \beta _2 } \right)^2 }}}
n31+b12d12(sinβ3)2\sqrt {1 + {{b_1^2 } \over {d_1^2 \left( {\sin \beta _3 } \right)^2 }}}
n41+b12d22(sinβ3)2\sqrt {1 + {{b_1^2 } \over {d_2^2 \left( {\sin \beta _3 } \right)^2 }}}
n51+d12b12(sinβ1)2\sqrt {1 + {{d_1^2 } \over {b_1^2 \left( {\sin \beta _1 } \right)^2 }}}
n61+d12b22(sinβ1)2\sqrt {1 + {{d_1^2 } \over {b_2^2 \left( {\sin \beta _1 } \right)^2 }}}
n71+d22b12(sinβ4)2\sqrt {1 + {{d_2^2 } \over {b_1^2 \left( {\sin \beta _4 } \right)^2 }}}
n81+d22b22(sinβ4)2\sqrt {1 + {{d_2^2 } \over {b_2^2 \left( {\sin \beta _4 } \right)^2 }}}

Comparison of the results obtained in this study with those obtained by Simoes et al_ (2014) by random finite limit analysis_

ScenarioMethodμNc [-]σNc [-]COVNc [-]
COVcu=0.5RFLA (Simoes et al. 2014)4.771.680.35
θ=8.0 mThis study5.192.140.41
COVcu=1.0RFLA (Simoes et al. 2014)3.721.230.33
θ=2.0 mThis study4.511.770.39
DOI: https://doi.org/10.2478/sgem-2019-0037 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 125 - 136
Submitted on: Dec 27, 2019
Accepted on: Feb 19, 2020
Published on: Jun 30, 2020
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Spatial averaging,
random fields,
random bearing capacity,
fluctuation scale,
failure mechanism
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2020 Marcin Chwała, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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